Efficient estimation and verification of quantum many-body systems

Loading...
Thumbnail Image

Date

2019-10-17

Journal Title

Journal ISSN

Volume Title

Publication Type

Dissertation

Published in

Abstract

Quantum systems and tensors share the property that the complexity of their description grows exponentially with the number of physical subsystems or tensor indices. This thesis discusses efficient methods for tensor reconstruction, quantum state estimation and verification, as well as quantum state and process tomography. The methods proposed here can be efficient in the sense that the resource requirements scale only polynomially instead of exponentially with the number of physical subsystems or tensor indices. In numerical and analytical calculations, matrix product state (MPS)/tensor train (TT), projected entangled pair state (PEPS), and hierarchical Tucker representations are used. The reconstruction and estimation methods are discussed in principle, their performance is evaluated with numerical simulations, and the quantum state in an ion trap quantum simulator experiment is estimated and verified.

Description

Faculties

Fakultät für Naturwissenschaften

Institutions

Institut für Theoretische Physik
Institut für Komplexe Quantensysteme

Citation

DFG Project uulm

JUSTUS / HPC-Cluster Theoretische Chemie / DFG / 236232410

License

Standard (ohne Print-on-Demand)

Keywords

Quantum state estimation, Quantum state tomography, Quantum process tomography, Ancilla-assisted process tomography, Quantum time evolution, Matrix product state, Matrix product operator, Tensor train, Projected entangled pair state, Tucker representation, Tensor reconstruction, Lieb-Robinson bound, Maximum likelihood estimation, Singular value thresholding, Quantenzustand, Spannungstensor, Maximum-Likelihood-Schätzung, Schwellenwert, Tensor fields, Quantum theory-Mathematics, Mathematical physics, DDC 500 / Natural sciences & mathematics, DDC 530 / Physics